Neither Tara Reade nor her claim she was sexually assaulted by Joseph R. Biden appear to be going away anytime soon, despite more than a week of denials and pushback from the presumptive Democratic presidential nominee and his supporters.

Mr. Biden is getting a taste of what it is like to be on the receiving end of a bombshell accusation and is embroiled in the middle of a he-said, she-said battle with no clear end in sight.

“The inability to prove or disprove it helps keep it alive,” said Aubrey Jewett, professor of political science at the University of Central Florida. “Assuming she sticks to her story and he sticks to his, it is unlikely there is going to be a smoking gun like in a court of law kind of proof.”

In an effort to shift focus back on to President Trump’s handling of the coronavirus, Mr. Biden went on MSNBC’s “Morning Joe” to personally respond to Ms. Reade’s allegation that as a U.S. senator in 1993, he pinned her against a wall, shoved his hand down her skirt and penetrated her with his fingers.

But he said the accusation has changed over time and is full of inaccuracies.

There have been mixed signs on how his response is playing with voters.

Morning Consult released a survey that found a quarter of Democrats — including 40% of those under the age of 45 — say the party should find another nominee.

A Monmouth Poll released last week found 37% of registered voters say the allegation is probably true while 32% say it probably is not, and the rest didn’t have an opinion.

Perhaps more worrisome for Mr. Biden is that 43% of independents said they believe Ms. Reade. That goes up to 45% among 18- to 45-year-olds — a group of voters that has been slow to warm to Mr. Biden.

The accusation has divided Democrats who had hoped to field a 2020 standardbearer who could provide a clear contrast with President Trump, who has faced a variety of allegations of sexual misconduct over the years.

“That puts an extra spotlight on whoever the Democrats’ nominee is — for them to be different, right?” Mr. Jewett said. “Because this has been on the point of attacks against Trump for many Democrats, many women in particular.”

Republicans have turned the accusation into attacks against down-ticket Democrats, casting them as hypocrites for believing the sexual harassment allegations leveled against Supreme Court Justice Brett Kavanaugh while glossing over an allegation against Mr. Biden.

New information came to light last week when a California newspaper located a 1996 court document that appears to back Ms. Reade’s claim that she felt she was the victim of sexual harassment while working as a staffer for Mr. Biden in the 1990s.

The record didn’t accuse Mr. Biden of anything, nor did it mention anything about sexual assault.

But the Tribune of Saint Luis Obispo found testimony that Ms. Reade’s then-husband Theodore Dronen provided in 1996 when he contested a restraining order she had filed against him after he filed for divorce.

In it, he says she told him about “a problem she was having at work regarding sexual harassment, in U.S. Senator Joe Biden’s office.”

Mr. Dronen said he struck up a relationship with Ms. Reade in 1993 when they worked in Washington as congressional staffers in different offices.

“On several occasions [Reade] related a problem she was having at work regarding sexual harassment, in U.S. Senate Joe Biden’s office,” Mr. Dronen said. “[Reade] told me that she eventually struck a deal with the chief of staff of the Senator’s office and left her position.”

“It was obvious that this event had a very traumatic effect on [Reade], and that she is still sensitive and effected by it today,” he said.

She plowed ahead with her version of events Thursday in an interview with former Fox News Host Megyn Kelly, saying she wished Mr. Biden would drop out of the race, and saying she would take a polygraph test if Mr. Biden followed suit.

“I’m not a criminal,” Ms. Reade said. “Joe Biden should take the polygraph.” “What kind of precedent does that set for survivors of violence? Does that mean we are presumed guilty and we all have to take polygraphs?”

“So I will take one if Joe Biden takes one,” she said. “But I’m not a criminal.”